CeVis
  1. Center of Complex Systems and Visualization
  2. Lehre
  3. Oberseminar

In dem regelmäßig stattfindenden Oberseminar tragen Gäste aus aller Welt über Forschungsarbeiten zu Themen vor, die mit der Arbeit von CeVis und MeVis in Verbindung stehen, und Mitarbeiter von CeVis und MeVis präsentieren ihre neusten Ergebnisse.


C(M)eVis Oberseminar am 15.10.1998


Datum: Donnerstag, der 15.10.1998
Zeit : 11.00 Uhr c.t.
Ort : Seminarraum Mandelbrot
Referent: Prof. Dr. Jean-Paul Allouche (CNRS, LRI, Orsay)
A SELF-SIMILAR ARITHMETICAL SET

In 1983 M. Cosnard and myself studied a set of binary sequences related to iterating real continuous unimodal functions. This set can be defined and studied in a purely (and elementary) combinatorial way. J. Shallit recently pointed to me that a very similar set was described recently by V. Komornik and P. Loreti (Amer. Math. Monthly 1998). We prove that these two sets are essentially the same. We describe this set, and we give an arithmetical translation (already mentioned in the 1983's paper) as follows. Let {y} be the fractional part of the real number y. Then the set of all x from the unit interval, for which for all k the condition 1-x <= {2^k x} <= x is satisfied, is self-similar and its least irrational element is the Thue-Morse number.


A. Rodenhausen, 5.10.1998